Friday, May 25, 2012

Concept and Object

Here I mentioned Frege's distinction between concept and object, and Anthony is rightly asking questions about it. How does direct reference relate to the distinction?

So I go back to Frege, and his famous essay. It's rather hard to get anything out of it, because he never properly defines the distinction. He says that his explanation is not meant as a proper definition. "One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance". What is logically simple cannot have a proper definition (as Aristotle also noticed).

But he does give the famous example of "all mammals are land dwellers", which will do for my purpose. He says that if 'all mammals' were the logical subject of 'are land dwellers', then to negate the whole sentence we should have to negate the predicate, giving "all mammals are not land-dwellers". That is obviously wrong, for this predicate negation gives the contrary of the sentence it negates, not the contradictory. Thus we must put the 'not' in front of the 'all', to give sentence negation. But no such distinction applies to genuinely singular subjects, i.e. object words. Indeed, he proves this by re-writing the original sentence as "the concept mammal is subordinate to the concept land-dweller". By negating the predicate we get "the concept mammal is not subordinate to the concept land-dweller", which is the contradictory of the original sentence. And so a useful criterion for determining whether an expression is a concept expression (a logical predicate) or an object expression (a logical subject) is to determine whether predicate negation is equivalent to sentence negation or not. If it is, then the grammatical subject is a logical subject as well. Otherwise it is a logical predicate.

With that test in mind, and on the assumption that proper names are logical subjects, direct reference immediately follows, as I shall show tomorrow.

6 comments:

First, the inequivalence of predicate and sentence negation within 'all mammals are land dwellers' could be said to arise because the expression 'all mammals' is quantified rather than conceptual. This complaint applies to yesterday's example of 'some man is running', also. However I wouldn't deny that 'mammals' plays a conceptual role within 'all mammals'.

But second, consider 'all the mammals in the zoo are land dwellers'. The same inequivalence arises yet 'all the mammals in the zoo' can quite reasonably be seen as a plural subject. Indeed the sentence can be seen as equivalent to a conjunction of singular assertions each bearing the name of a particular mammal or an appropriate demonstrative.

OK, I see Frege's point better now. But doesn't my second example show that the inequivalence arises out of the conjunctive structure of the sentence rather than the conceptual character of the subject? Try 'Bill and Ed are philosophers'. Same inequivalence but no hint of quantification/instantiation.

Well, that's not correct in the case of empty proper names. Predicate negation is not equivalent to sentence negation in the case of an empty proper name. An empty name is a logical predicate (which is not to say that it is a concept).